Please answer the below question in detail: A lossless transmission line with 75
ID: 2988288 • Letter: P
Question
Please answer the below question in detail:
A lossless transmission line with 75 Ohm characteristic impedance value is terminated by an unknown load ZL. If at a distance of 2.25 X from the load to the generator, we measure the value of the total voltage and it is20 volts and the value of total current is 0.4 amperes 1) Find voltage reflection coefficient at the input 2) Find V and I" at that point of the line 3) Can you find the load impedance? If it is possible to find, and if you think there is not enough information explain your answer 4) Find the value of the V" at the loadExplanation / Answer
Zo = characteristic impedance = 75 ohm
Zin = inpt impedance =V/I =20/0.4 = 50 ohm
a) Ti = reflection coefficient at input
= (Zin- Zo)/(Zin+Zo)
= (50-75)/(50+75)
= -0.2
2) V+ = V/(1+Ti) =20/(1-0.2) =25 v
I- =V+ x Ti/Zo = -0.2*25 /75 = -0.06 A
3) L = 2.25 *lemda
tan(2*pi *L / lemda) = tan(2*pi* 2.25) =tan(4.5*pi) =tan( 4*pi + pi/2)
Zin = Zo [ ZL +JZo *tan(2*pi *L / lemda)]/[Zo +JZL *tan(2*pi *L / lemda)]
= Zo [ ZL +JZo *tan(4.5pi)] /[Zo +JZL *tan(4.5pi)]
Zin = Zo^2/ZL
ZL = Zo^2/Zin = 75^2/50 =112.5 ohm
ZL = load impedance = 112.5 ohm
4) TL = reflection coefficent at load
= [ZL-Zo]/[ZL+Zo]
= 37.5/187.5
=0.2
VL = voltage at load = -J * Zo* I = -J * 75 *0.4 =-30 J
VL+ = *VL/(1+TL) =-25 J
VL- = VL+/TL = -25 J/0.2 = -125 J